Prove that a continuous random variable with a probability density function that is symmetric about a point

Question:

Prove that a continuous random variable with a probability density function that is symmetric about a point n has an expected value equal to the point of symmetry μ.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Probability And Statistics For Engineers And Scientists

ISBN: 9780495107576

3rd Edition

Authors: Anthony Hayter

See More Books

Question Posted: Jun 22, 2016 07:02 AM

See More Questions

Suppose that X is a continuous random variable with density function f. Show that E[|X - a|] is minimized when a is equal to the median of F. Write Now break up the integral into the regions where x...
This exercise will lead you through a proof of Chebyshevs inequality. Let X be a continuous random variable with probability density function f (x). Suppose that P(X < 0) = 0, so f (x) = 0 for x 0....
Let A be a continuous random variable with pdf f(x) and cdf F(x). For a fixed number xo, define the function Prove that g(x) is a pdf. (Assume that F(xo) f(2)/1- F(zo)] 9(=) = {e)/t I < 10. %3D
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
On your own or with a classmate, identify, draw, and explain a reverse channel with which you are familiar. What purpose does this reverse channel serve to businesses? To the community? To consumers?
Why should an effective tax be efficient? Responses so that people feel the tax is fairso that people feel the tax is fair so that everything is transparentso that everything is transparent so the...
Analyze the fuel consumption data in Table B. 18 for multicollinearity. y X2 X3 X4 xs X6 X7 Xg 343 0 52.8 811.7 2.11 220 261 87 1.8 356 1 52.8 811.7 2.11 220 261 87 1.8 344 0 50.0 821.3 2.11 223 260...
What are the advantages of establishing pay ranges, rather than specific pay levels, for each job? What are the drawbacks of this approach?
Some time ago my mother in law came to visit us. While visiting, I noticed her talent in knitting beautiful woolen scarves. I asked her if she was interested in selling them in our boutique and she...
Jenny Brown opened a law office, on July 1, 2010. On July 31, the balance sheet showed Cash $5,000, Accounts Receivable $1,500, Supplies $500, Office Equipment $6,000, Accounts Payable $4,200, and...
Consider again the archery problem discussed in Problem 2.2.9. What is the expected deviation from the center of the target? What is the median deviation? Problem 2.2.9 An archer shoots an arrow at a...
Recall Problem 2.1.1 I concerning the scheduling of appointments with a consultant. What is the expected value of the total number of appointments that have already been made over both days at the...
Decision trees can be used in the following applications: a. Credit risk scoring. b. Credit risk scoring and churn prediction. c. Credit risk scoring, churn prediction, and customer profile...
What is the Six Sigma approach to performance measurement?
If you worked in a culture that has difficulty accepting women as leaders, how should you address this issue?
When is interrupting appropriate?
Can you think of any teams that dont require clear, challenging goals, a team identity, and designated roles?
Coach Jim White (Kevin Costner) faces a daunting task providing effective leadership for his crosscountry high school team. Examine leadership styles, servant leadership, and the importance of...
Identify the two concepts that apply to the provision for unrealised profit.
Borrowing costs should be recognised as an expense and charged to the profit and loss account of the period in which they are incurred : A. If the borrowing costs relate to qualifying asset B. If the...
Hamilton County judges try thousands of cases per year. In an overwhelming majority of the cases disposed, the verdict stands as rendered. However, some cases are appealed, and of those appealed,...
Hamilton County judges try thousands of cases per year. In an overwhelming majority of the cases disposed, the verdict stands as rendered. However, some cases are appealed, and of those appealed,...
A study examined waiting times in the X-ray department for a hospital in Jacksonville, Florida. A clerk recorded the number of patients waiting for service at 9:00 A.M. on 20 consecutive days and...
How do I use voice commands to control my computer with the project of making a video?
Dan Mullen is employed by a mail-order distributor and reconditions used desktop computers, broadband routers, and laser printers. Dan is paid $12 per hour, plus an extra $6 per hour for work in...
Consider two series Yt and Y2t: Y = IIY-1 +6 Or more explicitly as: Aye Aya Yit Elt + Y2t 2t in which = [1, 2]' is IID with E(e) = 0 and E(ee'): [ 0 0 a) Write the system in levels Answer: A-AU-N b)...

Prove that a continuous random variable with a probability density function that is symmetric about a point

Question:

Step by Step Answer:

Let fx be a probability density f...View the full answer

Probability And Statistics For Engineers And Scientists

Students also viewed these Statistics questions